Large-scale metrology includes the measurement of coordinates over large distances, for example greater than the volume of a conventional coordinate measurement machine (CMM), which is typically limited to a cube of a few meters. There are many instances, for example in the aircraft industry, radio telescope and linear accelerator applications where measuring such distances is preferably accomplished with a high degree of accuracy. There are also field measurements of smaller scale which do not lend themselves to placement in a CMM, such as in situ measurements of machinery, outdoor measurements, shop floor measurements, etc.
The measurement of coordinates is typically accomplished by measuring a distance and two angles, as with a conventional surveying total station or laser tracking interferometer; the measurement of three orthogonal distances, as with a CMM; the measurement of angles from two locations on a known baseline, such as with theodolites; the measurement of spacing on a two-dimensional image projection from multiple locations, as with photogrammetry; the measurement of distance from three, or more, known locations on a baseline, as with multilateration; and various other manners.
One way to measure distances accurately is by using laser interferometry. In laser interferometry a coherent, monochromatic light beam from a laser is split into two beams using a beamsplitter. One beam, the reference beam, is focused onto a photosensitive detector. The second or measurement beam, is allowed to travel through space and strike a reflector positioned in space at the first of two measurement points. The reflector is adjusted to return the reference beam to the surface of the photosensitive detector. Here the reference and reflected measurement beams interfere. The target reflector can then be moved to the second point to be measured. As the target moves, the reflected measurement light beam is continuously focused onto the photosensitive detector, interfering with the reference beam. By electrically measuring the periodic variation of the detector output, one can measure differential lengths from the initial target position as multiples and fractions of the wavelength of the illuminating source.
In all of these laser interferometry devices, the reflective target is preferably oriented to return the reflected measurement beam to the photosensitive target of the detector from a wide range of beam angles. Typically, a retroreflector, such as a hollow three-mirror reflector, comprised of three carefully aligned orthogonal mirrors (typically on the order of one arc second), is used to return the beam. The retroreflector may have slightly less accuracy than a single flat mirror but only requires that the operator align the device so as to point towards the detector within a cone of perhaps 30–40 degrees in width. The reflected beam from the retroreflector undergoes reflections from all three orthogonal mirrors and has the interesting property that the return beam will emerge traveling parallel to the incoming beam, in the opposite direction, and displaced from the incoming beam by a distance of twice the distance from the incoming beam to the retroreflector apex, i.e., symmetrically about a parallel beam through the apex. The optical path length, and thus the time of flight, is virtually the same as the distance to the retroreflector apex. Therefore, the measurement is physically associated with the physical location of the retroreflector apex.
Electronic distance measurement (EDM) is commonly achieved by measuring the time of flight of an electromagnetic wave, such as a laser beam or microwave radar, to a target retroreflector or the scattered reflection from a passive target. Most conventional surveying instruments employ a retroreflector target in order to clearly define the measurement point, improve the signal-to-noise ratio of the return signal, and thus operate at reduced power. While typically not as accurate as the laser interferometer, EDM offers a major advantage over the interferometer for many applications. Unlike the interferometer, which inherently measures a differential distance—and thus must be used in a fringe counting integration mode to measure between two points without a break in the signal, EDM measures the absolute distance between the instrument and target. Thus, there is no requirement to integrate over a path while physically moving the target retroreflector through the measurement volume. This allows EDM to be used to measure multiple targets by switching between targets at will. The operating range of conventional EDMs are kilometers, while the operating range of typical laser interferometers are less than 100 meters.
A number of laser interferometer and electronic distance measurement applications desire an even wider angle of acceptance or multiple retroreflectors. A problem with using multiple retroreflectors is that not all of the retroreflectors can be located at a common measurement point. When the measurement axis does not pass through the measurement point, the resulting measurements are sensitive to rotations of the object and/or angle between the instrument and object, i.e., the Abbe error (See Ted Busch, Fundamentals of Dimensional Metrology (Delmar, 1988)).
Surveying equipment manufacturers have assembled solid glass retroreflectors, such as the Leica™ GRZ4 360 degree prism. However, as described in L. A. Kivioja, The EDM Corner Reflector Constant is Not Constant, Surveying and Mapping 143–55 (June 1978) and D. C. Hogg, Optical Center of a Glass Three-mirror: Its Measurement, Applied Optics, 15(2):304–305 (February 1976), the glass offset, or extra delay due to the reduced speed of light in glass, is a function of the incident angle, and the coverage overlaps between adjacent retroreflectors, so there is a significant Abbe error for the GRZ4.
Laser interferometers are typically calibrated in a back-to-back retroreflector configuration, where the rotation of the retroreflectors is constrained. For example, the National Institute of Standards and Technology (NIST) has built a Laser Rail Calibration System (Larcs) for calibrating laser trackers against an interferometer on a linear rail. Tracking laser interferometers are discussed in U.S. Pat. Nos. 4,714,339 to Lau et al.; and 4,790,651 to Brown et. al. Larcs uses two spherically mounted retroreflectors (SMRs) (described in more detail below), in a back-to-back configuration on a carriage, to build a bidirectional retroreflector assembly, i.e., one direction fixed for the reference interferometer parallel to the rail, and the other free to rotate in a nest to accommodate the laser tracker under test.
The Abbe error is minimized by mounting the two retroreflectors as close as practical and constraining the carriage to a rail system to minimize rotations of the assembly. However, for portable rails, the uncertainty due to the Abbe error is estimated to be a significant part of the total error budget.
NASA has built custom hollow retroreflector assemblies with a common physical reflection point, and thus eliminated the Abbe error. See Schmidtlin et. al., Novel Wide Field-of-View Laser Retroreflector for the Space Interferometry Mission, Conference on Astronomical Interferometry, Vol. 3350, 81–88, SPIE, 1998 and NASA Jet Propulsion Lab, Wide-Angle, Open-Faced Retroreflectors for Optical Metrology, Photonics Tech Briefs, 15a–16a, (March 1999).
These solve the Abbe error problem for some classes of measurements. However, since these retroreflectors share a common physical point, they sacrifice part of the center aperture, are difficult to build, are difficult to reference to an outside mechanical point, are expensive for routine applications, and the directions are not adjustable.
Gelbart et. al. in U.S. Pat. Nos. 5,305,091 and 5,920,394 describe an “omnidirectional retroreflector” pair combined with a fixed probe. By multilaterating on the pair of retroreflectors, the probe coordinate is calculated. The omnidirectional retroreflectors, described in the '091 patent, “consist of two concentric spheres made of transparent material and having the refractive index of the inner sphere higher than the refractive index of the outer sphere, the outside sphere coated with a partially reflective coating.”
As described by Takatsuji et. al., Whole-Viewing-Angle Cat's-Eye Retroreflector as a Target of Laser Trackers, Measurement Science Technology, 1O:N87–N90 (1999), ideal omnidirectional spherical retroreflectors have recently been built from high index of refraction materials. Unfortunately, the glass is difficult to work, expensive, and the return power is low due to the spherical aberration and small working aperture, as well as the low reflection coefficient of the glass/air interface on the back side of the sphere, i.e., most of the power is transmitted through the sphere.
Laser trackers incorporate a laser interferometer with an automated mirror system to track a retroreflector. The interferometer measures differential range very accurately, with the fundamental limitation being the uncertainty of the index of refraction—which is typically in the 1 ppm range.
The angle measurements are somewhat less accurate. The fundamental limitation is atmospheric turbulence and temperature gradients bending the beam. There are also practical limitations with the encoders, mechanical system, beam quality, gravitational vector reference frame, etc.
Nakamura et al., A Laser Tracking Robot Performance Calibration System Using Ball-Seated Bearing Mechanisms and a Spherically Shaped Cat's-Eye Retroreflector, Review of Scientific Instruments, 65(4):1006–1011, (April 1994), points out that for a distance measurement uncertainty of δr, in an ideal orthogonal trilateration measurement, the uncertainty volume is (δr)3. For two angles and a distance measurement, the uncertainty volume is (rδθ)2δr. For example, for a typical distance measurement uncertainty of 1 ppm (δr/r=10−6) and an angle uncertainty of one arc second (˜5×10−6 radians), the trilateration uncertainty, for three equal distances r, the uncertainty volume would beδv=r310−18whereas the uncertainty volume for two angles and a distance would beδv=25r310−18,or 25 times greater than the trilateration uncertainty volume—hence the inherent potential improvement in accuracy by using multiple distance measurements. In practice, there are two primary obstacles to achieving this huge improvement. Conventional retroreflectors do not support simultaneous measurements in the three orthogonal directions, and in actual field conditions it can be hard to mount an instrument on a stable tower or structure.
U.S. Pat. Nos. 5,530,549 and 5,861,956 to Brown et al., describe a probing retroreflector in which the distance to a probe tip can be determined. In Brown et al. a line between a retroreflector and a probe tip is bisected by a single mirror. The length of the optical path between the mirror and the probe tip is the same as the length of the optical path between the mirror and the apex of the retroflector. The system has allowed the use of retroreflectors in spaces that can not normally be reached by a typical retroreflector. This system, however, does not allow measurements to be simultaneously taken from different directions.
Laser trackers typically use spherically mounted retroreflector (SMR) targets. These are typically hollow or cat's-eye type retroreflectors, with the optical centers carefully located in the center of the spherical mounting—thus allowing the optical measurements to be related to the physical center of the sphere. Hollow SMRs, such as those built by PLX Inc.® are more economical than cat's-eye SMRs, but have a reduced angle of acceptance and thus are more susceptible to dropping the laser interferometer beam while tracking.
An improvement in the accuracy of the laser tracker (or EDM) is to use multiple instruments and/or augment with additional information, e.g., known artifacts, stable bench marks, hydrostatic leveling, or other constraints. For three or more instruments, oriented in the proper baselines, the less accurate angle measurements can be neglected or weighted less in a least squares, or more sophisticated, reduction.
While crosstalk between instruments is not a problem using multiple laser trackers on a common SMR, the relatively small angle limitation of even the cat's-eyes makes the instrument baselines unfavorable for high accuracy multilateration measurements, and of course the Abbe error is the limitation for conventional assemblies of SMRs.
As described by Parker et. al., Metrology System for the Green Bank Telescope, in Proceedings ASPE 1999 Annual Meeting, pages 21–24 (American Society for Precision Engineering, 1999). The Robert C. Byrd Green Bank Telescope large-scale metrology system was designed to operate as a multilateration system employing 18 laser ranging instruments measuring ranges to cardinal points on the moving telescope. While some paths are physically blocked by the structure, it behooves the designers to use multidirectional retroreflectors in order to maximize the number of independent measurements, and thus strengthen the calculation of cardinal point coordinates.
The increasing interest in multilateration, using laser trackers or other EDMs, has created a need for less expensive and more practical multidirectional retroreflectors with zero Abbe error.
In addition, in some retroreflector applications it may be desirable to attenuate the return beam from the retroreflectors. For example, in some electronic distance measurement applications, the dynamic range may be such that the signal is preferably attenuated for close-range measurements in order to avoid non-linearities in the detector electronics.
To account for time of flight or, alternatively, phase shift through the attenuator, any attenuating filter may need correction for the group index of refraction of the attenuating medium. Also, the cosine theta error for the thickness of the filter is preferably avoided. Finally, additional surfaces can introduce additional reflections which can introduce phase errors and make the retroreflector sensitive to orientation.